First Steps Towards an Imprecise Poisson Process
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Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:175184, 2019.
Abstract
The Poisson process is the most elementary continuoustime stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate interval and let it characterise two nested sets of stochastic processes. We call these two sets of stochastic process imprecise Poisson processes, explain why this is justified, and study the corresponding lower and upper (conditional) expectations. Besides a general theoretical framework, we also provide practical methods to compute lower and upper (conditional) expectations of functions that depend on the number of events at a single point in time.
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